A240683 Number of forests with n labeled nodes and 6 trees.

1, 21, 378, 7056, 143325, 3207897, 79170399, 2146836978, 63641666088, 2051450651250, 71530799628288, 2684845732979592, 107992630908804096, 4636019437800293718, 211623646464000000000, 10237455825414473977524, 523244238837133507448832, 28177157277452320985386539

Offset: 6

Author

Alois P. Heinz, Apr 10 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..200

Crossrefs

Column m=6 of A105599. A diagonal of A138464.

Programs

Maple

T:= proc(n, m) option remember; `if`(n<0, 0, `if`(n=m, 1,
      `if`(m<1 or m>n, 0, add(binomial(n-1, j-1)*j^(j-2)*
       T(n-j, m-1), j=1..n-m+1))))
    end:
a:= n-> T(n, 6):
seq(a(n), n=6..30);

Mathematica

Table[n^(n-12) * (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^5 + 40*n^4 + 835*n^3 + 10960*n^2 + 87636*n + 332640)/3840,{n,6,25}] (* Vaclav Kotesovec, Sep 06 2014 *)

Formula

a(n) = n^(n-12) * (n-5)*(n-4)*(n-3)*(n-2)*(n-1)*(n^5 + 40*n^4 + 835*n^3 + 10960*n^2 + 87636*n + 332640)/3840. - Vaclav Kotesovec, Sep 06 2014